Infinitely stretchable elastic band

[orlan2r]

Imagine an infinitely stretchable elastic band where one end is attached to a vertical wall and the other on a horse, as shown in figure. On the elastic band, very close to the wall, there is a snail. If we assume that the initial length of the band is L, and the horse and snail start moving with constant rapideces v y u (v > u), respectively, how long time the snail reached the horse?

 

[berkeman]

Is this a brain teaser or for schoolwork? It doesn't really fit in the Classical Physics forum.

 

[AlephZero]

There was a recent thread about the same brain teaser.
https://www.physicsforums.com/showthread.php?t=723340

 

[orlan2r]

The problem referred by AlephZero is simliar but is purely mathematical.
I propuse a physics brain teaser.
In this case we can say the snail's movement respect to the Earth result of composition of movements: their own movement respect of the elastic band and the movement of the point of the elastic band on which is located

 

[PJC01]

I would like to clarify a few things about this scenario before providing a response. Firstly, an infinitely stretchable elastic band is not a physical possibility as all materials have a limit to their stretchability. However, for the sake of this hypothetical situation, let us assume that the elastic band has an extremely high stretchability and behaves as described.

Assuming that the elastic band is attached to a vertical wall and is infinitely stretchable, the snail would be able to reach the horse in a finite amount of time. This is because the elastic band would continuously stretch as the horse moves away from the wall, allowing the snail to travel a greater distance in a shorter amount of time.

The time it takes for the snail to reach the horse would depend on the relative velocities of the horse and the snail. If the horse is moving at a much faster velocity than the snail, it would take a shorter amount of time for the snail to reach the horse. On the other hand, if the snail is moving at a faster velocity than the horse, it would take a longer time for the snail to reach the horse.

In terms of the specific time it would take for the snail to reach the horse, it would also depend on the initial length of the elastic band (L) and the exact values of the velocities of the horse (v) and the snail (u). A mathematical equation could be derived to calculate the time taken, but it would require more information and assumptions about the elastic band and the movement of the horse and snail.

Overall, while an infinitely stretchable elastic band is not physically possible, this hypothetical scenario allows us to think about the concept of time and motion in a unique way. It also highlights the importance of considering all variables and limitations when making scientific assumptions and calculations.